The Delft Sand, Clay & Rock Cutting Model, 2019a

The Delft Sand, Clay & Rock Cutting Model.
Wismer and Luth (1972A) and (1972B) investigated the inertia forces term I of the total cutting forces. The
following equation is derived:
2 sin( )
I s vc hi
w
sin( )
(3-16)
The cohesive and the adhesive forces C and A can be determined with soil mechanical experiments. For the
cohesive and adhesive forces the following equations are valid:
ch i w
C sin( )
ah b w
A
sin( )
(3-17)
(3-18)
The gravitational force G (weight submerged) follows from:
b i i
G s w ghi
w
sin( ) sin( ) 2 sin( )
sin( )
h h sin( ) h cos( )
(3-19)
The gravitational force G (dry weight) follows from:
sin( )
h h sin( ) h cos( )
b i i
G s ghi w
sin( ) sin( ) 2 sin( )
(3-20)
This is in accordance with the area that is used for the water pore pressure calculations in the case of water saturated
sand (see Figure 6-7).
3.4. The Curling Type.
In some soils it is possible that the Curling Type of cutting mechanism occurs. This will happen when the layer
cut is relatively thin and there is a force on the blade of which the magnitude depends on the blade height, like the
adhesive force or the pore pressure force in the case of a cavitating cutting process. In soils like clay and loam, but
also in rock under hyperbaric conditions this may occur. Figure 3-8 shows this Curling Type. The question now
is, what is the effective blade height hb,m where the soil is in contact with the blade. To solve this problem, an
additional equation is required. There is only one equation available and that is the equilibrium equation of
moments on the layer cut. Figure 3-9 shows the moments acting on the layer cut. In the case of clay, loam or
hyperbaric rock, the contribution of gravity can be neglected.
The equilibrium of moments when the gravity moment is neglected is:
N W R N W R
(3-21)
1 1 1 2 2 2
The arms of the 2 moments are:
R
h
1 i
1 , R2
sin
h
2 b,m
sin
(3-22)
This gives the equilibrium equation of moments on the layer cut:
Page 80 of 454 TOC Copyright © Dr.ir. S.A. Miedema